Relief could be on the way for stressed travelers driving to Logan International Airport as airport managers have finalized the location of two garages that will add around 5,000 parking spaces.

Massachusetts Port Authority chief executive Thomas Glynn said the agency would build one garage on a surface lot next to Terminal E that would have around 1,250 spaces but eliminate 240 existing spaces. The second, a much-larger project with about 4,000 spaces, would involve expanding the Economy garage along the Service Road near the entrance to the airport.

The two projects will cost $250 million, and Glynn said Massport could file plans with state environmental regulators within two months. However, the start of construction could be as much as two years off, in part because Massport first needs state officials to amend a parking freeze that limits commercial spaces at the airport to 18,640.

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Massport officials have argued that lifting the parking freeze could result in fewer cars coming through Logan. Right now, the agency said, many travelers are still getting rides to their flights, and each drop-off and pickup is its own separate trip in and out of the airport; driving themselves and parking at Logan would reduce some of those trips.

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“They’ve made a very strong case to the business community that environmentally it is more sound than having people do drop-off and pickup,” said Dan O’Connell, chief executive of the Massachusetts Competitive Partnership.

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The parking shortage has long frustrated travelers such as Richard Doherty, president of the Association of Independent Colleges and Universities in Massachusetts. He was planning to drive to Logan Tuesday morning for a flight to Washington but after learning the garages were full Monday, assumed there would be no room the next day. So he will probably take an Uber instead.

“It limited my choices of how I was going to get to the airport,” Doherty said. The parking shortage “is not limiting the number of cars going to the airport. It just limited which car is going to the airport.”

When drivers show up at Logan and the garages are full, Massport often diverts them to overflow lots farther from the terminals or arranges for valets to park their cars in rows within the garages. On particularly busy days, travelers can be shunted to a lot at Suffolk Downs.

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A Massport spokesman said drivers were diverted to overflow lots or had their cars valeted on 97 days in the first 10 months of 2016, compared to 93 for the same period last year, even though Massport recently added about 1,700 spaces to Logan’s central parking complex.

The two locations for the new garages were selected from six possible sites Massport had been examining. Glynn said they were picked after consulting with Logan neighbors.

However, East Boston residents active in a Logan watchdog group questioned whether the garages would be an improvement environmentally. Chris Marchi, a resident with the neighborhood group Airport Impact Relief Inc., is skeptical the garages would result in less traffic through his neighborhood and questioned whether Massport is more interested in the additional parking revenue.

“The fact that they’re asking for more spaces is just because they want to get paid for that,” Marchi said. “They are focused on growth, and the growth is out of control.”

Massport is also weighing improvements to mass transit options, including increasing its subsidies for Silver Line service to the airport and considering new stops for its Logan Express bus service.

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Massport is also in the midst of a major renovation of Terminal E to keep up with the flood of new international travelers. The agency is building a second level at three gates, to accommodate larger jets. It also plans to eventually add seven new gates and a pedestrian connector to the Blue Line MBTA station.